Find lim_(x rarr4)(2-sqrt(4x-12))/(x-4). Choose 1 answer: (A) 2 (B) 1 (c) -1 (D) The limit doesn't exist

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Find  lim_(x rarr4)(2-sqrt(4x-12))/(x-4). Choose 1 answer: (A) 2 (B) 1 (c) -1 (D) The limit doesn't exist

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Substitution Check: First, let's try to directly substitute x = 4 into the limit expression to see if it results in an indeterminate form. lim_(x -> 4)(2 - sqrt(4x - 12)) / (x - 4) = (2 - sqrt(4*4 - 12)) / (4 - 4) = (2 - sqrt(16 - 12)) / 0 = (2 - sqrt(4)) / 0 = (2 - 2) / 0 = 0 / 0 This is an indeterminate form, so we cannot directly evaluate the limit by substitution.Algebraic Manipulation: Since we have an indeterminate form of 0/0, we need to use algebraic manipulation to simplify the expression. We can multiply the numerator and the denominator by the conjugate of the numerator to eliminate the square root. The conjugate of the numerator 2 - sqrt(4x - 12) is 2 + sqrt(4x - 12). We will multiply both the numerator and the denominator by this conjugate. lim_(x -> 4)((2 - sqrt(4x - 12))(2 + sqrt(4x - 12))) / ((x - 4)(2 + sqrt(4x - 12)))Numerator Multiplication: Now, let's perform the multiplication in the numerator, which is a difference of squares. (2 - sqrt(4x - 12))(2 + sqrt(4x - 12)) = 2^2 - (sqrt(4x - 12))^2 = 4 - (4x - 12) = 4 - 4x + 12 = 16 - 4xSimplified Limit: We can now rewrite the limit with the simplified numerator. lim_(x -> 4)(16 - 4x) / ((x - 4)(2 + sqrt(4x - 12)))Factor Out -4: Notice that we can factor out a -4 from the numerator to cancel out the (x - 4) term in the denominator. lim_(x -> 4)(-4(x - 4)) / ((x - 4)(2 + sqrt(4x - 12))) = lim_(x -> 4)(-4) / (2 + sqrt(4x - 12))Final Substitution: Now we can directly substitute x = 4 into the simplified limit expression. lim_(x -> 4)(-4) / (2 + sqrt(4*4 - 12)) = (-4) / (2 + sqrt(16 - 12)) = (-4) / (2 + sqrt(4)) = (-4) / (2 + 2) = (-4) / 4 = -1

Find $\lim _{x \rightarrow 4} \frac{2-\sqrt{4 x-12}}{x-4}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $2$ $\newline$ (B) $1$ $\newline$ (C) $-1$ $\newline$ (D) The limit doesn't exist

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Find lim⁡x→42−4x−12x−4 \lim _{x \rightarrow 4} \frac{2-\sqrt{4 x-12}}{x-4} limx→4​x−42−4x−12​​.\newlineChoose 111 answer:\newline(A) 222\newline(B) 111\newline(C) −1-1−1\newline(D) The limit doesn't exist

Find $\lim _{x \rightarrow 4} \frac{2-\sqrt{4 x-12}}{x-4}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $2$ $\newline$ (B) $1$ $\newline$ (C) $-1$ $\newline$ (D) The limit doesn't exist